As is known, multi-spectral images are images acquired by Remote Sensing (RS) radiometers, each acquiring a digital image (in remote sensing, called a scene) in a small band of visible spectra, ranging from 0.4 μm to 0.7 μm, called red-green-blue (RGB) region, and going to infra-red wavelengths of 0.7 μm to 10 or more μm, classified as NIR (Near InfraRed), MIR (Middle InfraRed), FIR (Far InfraRed) or TIR (Thermal InfraRed). A multi-spectral image is hence a collection of several single-spectral (single-band or monochrome) images of the same scene, each taken with a sensor sensitive to a different wavelength.
Different fire detection techniques, based on threshold criteria and contextual algorithms, have been developed for multi-spectral polar sensors and, in the last years, for geostationary sensors. For a detailed discussion of these techniques reference may, for example, be made to Kaufman, Y. J., Justice, C. O., Flynn, L. P. Kendal, J. D., Prins, E. M., Giglio, L. Ward, D. E. Menzel, W. P. and Setzer, A. W., 1998, Potential global fire monitoring from EOS-MODIS, Journal of Geophysical Research, 103, 32215-32238, and Giglio, L., Descloitres, J., Justice, C. O. & Kaufman, Y. J. (2003), An enhanced contextual fire detection algorithm for MODIS, Rem. Sen. Environment, 87:273-282.
Multi-spectral sensors on polar satellites are characterized by a relatively high spatial resolution, but, due to the long revisit time of polar satellites, the promptness needed for effective fire detection purposes cannot be achieved, even combining all existing multi-spectral polar sensors. On the contrary, multi-spectral geostationary sensors provide very frequent acquisitions, e.g. every 15 minutes for the MSG SEVIRI (Spinning Enhanced Visible and Infra Red Imager) sensor, though characterized by a lower spatial resolution (3×3 km2 and above for infrared channels), which could prevent small fires from being detected.
In order to overcome the spatial resolution limitations, a physical model-based approach for sub-pixel fires detection from geostationary sensors data was recently proposed by E. Cisbani, A. Bartoloni, M. Marchese, G. Elisei, A. Salvati, Early fire detection system based on multi-temporal images of geostationary and polar satellites, IGARSS 2002, Toronto, 2002, and Calle, A., Casanova, J. L., Moclan, C., Romo, A. J., Costantini, M., Cisbani, E., Zavagli, M., Greco, B., Latest Algorithms and Scientific Developments for Forest Fire Detection and Monitoring Using MSG/SEVIRI and MODIS Sensors, IEEE, 2005, 118-123.
In particular, an analytic Radiative Transfer Model (RTM) is proposed which characterizes the radiative phenomena that determine the sensor-detected energy, expressed by means of radiances Rλ (W/m2/sr/μm) for each band λ in atmospherically transparent windows in Near Infrared (NIR), Middle Infrared (MIR) and Thermal Infrared (TIR) spectral regions. As shown in FIG. 1(a), the radiance Rλ collected by a remote satellite sensor is the sum of the solar radiance RS,λ reflected by the ground, the atmospheric thermal radiance RA,λ (both the up-welling and the down-welling components), and, finally, the thermal emission of the ground. Given the background temperature TB, the emissivity ελ of the Earth's surface, and the transmittance of the atmosphere τλ between the Earth's surface and the sensor, the RTM can be expressed as:Rλ=ελτλBλ(TB)+RA;λ+RS;λ,  (1)where, Bλ(T) is the Planck black-body emission at temperature T and wavelength λ. Other RTM models can be exploited as well.
According to C. C. Borel, W. B. Clodius, J. J. Szymanski and J. P. Theiler, Comparing Robust and Physics-Based Sea Surface Temperature Retrievals for High Resolution, Multi-Spectral Thermal Sensors Using one or Multiple Looks, Proc. of the SPIE '99, Conf. 3717-09, the main contribution to the transmittance τλ in the atmospheric windows in the NIR and TIR regions comes from the atmospheric water vapor content and the relations between transmittance and water vapor can be quite appropriately be parameterized by the following expression:
                                          τ            λ                    ⁡                      (                          W              ,              ϑ                        )                          =                  exp          ⁡                      (                          -                              [                                                                            A                      λ                                                              cos                      ⁢                                                                                          ⁢                      ϑ                                                        +                                                                                    B                        λ                                            ⁡                                              (                                                  W                                                      cos                            ⁢                                                                                                                  ⁢                            ϑ                                                                          )                                                                                    C                      λ                                                                      ]                                      )                                              (        2        )            where W is the total water vapour along the path ending/starting at/from the examined pixel and having a zenith angle θ. Parameters Aλ, Bλ and Cλ depend (at least) on the wavelength λ and can be estimated via several MODTRAN (MODerate resolution atmospheric TRANsmission) simulations (computer program designed to model atmospheric propagation of electromagnetic radiation from 100-50000 cm−1 with a spectral resolution of 1 cm−1) and regression methods. Other models/methods to estimate τλ can be considered.
The water vapour W content can be estimated as described in Eumetsat Satellite Application Facility, Software Users Manual of the SAFNWC/MSG: Scientific part for the PGE06, SAF/NWC/INM/SCI/SUM/06, issue 1.0, January 2002, but other methods can be considered.
The solar term RS,λ can be calculated as described in the aforementioned Potential global fire monitoring from EOS-MODIS:
                              R                      S            ,            λ                          =                              E                          S              ,              λ                                ⁢                      cos            ⁡                          (                              ϑ                S                            )                                ⁢                                    τ              λ                        ⁡                          (                              z                SE                            )                                ⁢                                    1              -                              ɛ                λ                                      π                    ⁢                                    τ              λ                        ⁡                          (                              z                ED                            )                                                          (        3        )            where the ES,λ is the Sun radiance at the top of the atmosphere, τλ (zSE) is the transmittance along the path between Sun and Earth's surface, τλ (zED) is the transmittance along the path between Earth's surface and satellite sensor, and ελ is the emissivity of the Earth's surface. Other models/methods can be exploited to calculate RS,λ.
The atmospheric radiance contribution RA,λ describes a complex phenomenon, characterized by smoke, aerosol, and local atmospheric temperatures hard to be modelled. A possible model is the following:
                              R                      A            ,            λ                          =                                                                              (                                      1                    -                                          ɛ                      λ                                                        )                                ⁢                                                                            τ                      λ                                        ⁡                                          (                                              z                        ED                                            )                                                        ⁡                                      [                                          1                      -                                                                        τ                          λ                                                ⁡                                                  (                                                      z                            TOA                                                    )                                                                                      ]                                                  ⁢                                                      B                    λ                                    ⁡                                      (                                          T                      A                                        )                                                              ︸                                      down              -              welling                                +                                                                      [                                      1                    -                                                                  τ                        λ                                            ⁡                                              (                                                  z                          ED                                                )                                                                              ]                                ⁢                                                      B                    λ                                    ⁡                                      (                                          T                      A                                        )                                                              ︸                                      up              -              welling                                                          (        4        )            where, referring to FIG. 1(b), the τλ (zTOA) is the transmittance along the vertical path between the Earth's surface and the top of the atmosphere, τλ (zED) is the transmittance along the path between the Earth's surface and the satellite sensor, and ελ, as in the foregoing, is the ground emissivity.
The Dozier formulation as described in J. Dozier, A Method for satellite identification of surface temperature fields of subpixel resolution, Remote Sensing of Environment, 11 (1981) 221-229 and applied to equation (1) (or to other RTM models) makes a sub-pixel description of the radiative process possible, considering the fire extension (pixel fraction f of a pixel of radiance acquired by the satellite sensor) and fire temperature TF:Rλ=εF;λ·τλ·Bλ(TF)·f+εB;λ·τλ·Bλ(TB)·(1−f)+RA;λ+RS;λ,  (5)where εF,λ and εB,λ are the fire and the background emissivities, respectively, at the wavelength λ.
According to the aforementioned Early fire detection system based on multi-temporal images of geostationary and polar satellites, if two successive acquisitions are considered, the Dozier formulation (5) can be written as follows:ΔRλ,t≡Rλ,t−Rλ,t−Δt=ελ·τλ,t·[Bλ(TF)−Bλ(TB)]·Δf  (6)where t and t−Δt denote two close acquisition times, and Δf=ft−ft−Δt, and where the following assumptions are done:                the background temperature TB is constant between two consecutive acquisitions (within 15 minutes for MSG SEVIRI data);        the fire emissivity is the same as the non-burning surface emissivity; and        the solar and the atmospheric terms (RS,λ, RA,λ) are considered constant between two consecutive acquisitions (within 15 minutes for MSG SEVIRI data).        
The introduced RTM (1) and equations (2), (3), (4), (5), (6) are reliable only if no clouds are in the analyzed scene. Therefore, a reliable cloud masking procedure is necessary to identify the acquisitions that are compatible with the physical model assumptions. Many techniques have been developed for cloud masking by exploiting polar or geostationary sensors. Basically, all these techniques are based on the application of threshold criteria to analytic relations among the different bands of a single acquisition. Methods to retrieve such relations among the spectral bands can be based on physical models or on learning methods based on neural networks, Bayesian networks, support vector machines, all of which require a pre-processing phase for the system training. Also contextual techniques that exploit the spatial information are known in literature.